#15431: Transversal Design TD(6,12)
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | 8273741e4f9cd86c788e2769084c954c24b1c8cf
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/15431 |
Dependencies: |
#15287 #15368 |
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Comment (by vdelecroix):
Replying to [comment:32 ncohen]:
> Yo !
>
> > - Reading the definition, I do not understand where `lambda` comes
from (in both bibd and td)
>
> As you wish. What about this ?
Fantastic!
> > - In `transversal_design` you do not specify whether the groups `V_i`
are disjoint or not. What is the convention? It should be said what is the
implementation in Sage (e.g. if I am using `is_transversal_design` I want
to know what I am testing).
>
> Well, it is the convention to have them disjoint, plus I used `\sqcup`
instead of `\cup`, plus you can actually deduce that they are disjoint
from the definition : if two groups intersect on one element, then a set
which contain it cannot have cardinality k as it must intersect each group
at most once, and there are k groups.
> I added a "disjoint" somewhere in the definition to make it clearer.
> > (e.g. if I am using is_transversal_design I want to know what I am
testing).
>
> Is there something unclear in the documentation of
`is_transversal_design` ?
>
Let me mention that `\sqcup` does not mean that they are disjoint but that
you take the [[http://en.wikipedia.org/wiki/Disjoint_union|disjoint
union]]. The set `A \sqcup A` is perfectly valid and will have cardinality
twice the one of `A`. So I would actually prefer a `\cup` if it is what
you intended to do.
The documentation is much better in `is_transversal_design` because of the
NOTE block. But there is nothing in `transversal_design`. Could you do a
copy/paste or something.
(For me, it would be clearer for a TD to be a subset of `V1 x V2 x ... x
Vk` but let us stick to conventions).
--
Ticket URL: <http://trac.sagemath.org/ticket/15431#comment:34>
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